Problem: What do the following two equations represent? $x+2y = 1$ $-4x-8y = -4$
Solution: Putting the first equation in $y = mx + b$ form gives: $x+2y = 1$ $2y = -x+1$ $y = -\dfrac{1}{2}x + \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $-4x-8y = -4$ $-8y = 4x-4$ $y = -\dfrac{1}{2}x + \dfrac{1}{2}$ The above equations turn into the same equation, so they represent equal lines.